Weight 2 CM newforms as p-adic limits

The Ramanujan Journal - Previous works have shown that certain weight 2 newforms are p-adic limits of weakly holomorphic modular forms under repeated application of the U-operator. The proofs of...     

Characterization and optimization of a positively charged poly (ethylene glycol)diacrylate hydrogel as an actuating muscle tissue engineering scaffold

Hydrogels have been used for many applications in tissue engineering and regenerative medicine due to their versatile material properties and similarities to the native extracellular matrix. Poly (ethylene glycol) diacrylate (PEGDA) is an ionic electroactive polymer (EAP), a material that responds to an electric field with a change in size or shape while in an ionic solution, that may be used in the development of hydrogels. In this study, we have investigated a positively charged EAP that can bend without the need of external ions. PEGDA was modified with the positively charged molecule 2‐(methacryloyloxy)ethyl‐trimethylammonium chloride (MAETAC) to provide its own positive ions. This hydrogel was then characterized and optimized for bending and cellular biocompatibility with C2C12 mouse myoblast cells. Studies show that the polymer responds to an electric field and supports C2C12 viability.     

Electrical conductivity,impedance, and percolation behavior of carbon nanofiber and carbon nanotube containing gellan gum hydrogels

The electrical impedance behavior of gellan gum (GG), GG–carbon nanotube, and GG–carbon nanofiber hydrogel composites is reported. It is demonstrated that the impedance behavior of these gels can be modeled using a Warburg element in series with a resistor. Sonolysis (required to disperse the carbon fillers) does not affect GG hydrogel electrical conductivity (1.2 ± 0.1 mS/cm), but has a detrimental effect on the gel's mechanical characteristics. It was found that the electrical conductivity (evaluated using impedance analysis) increases with increasing volume fraction of the carbon fillers and decreasing water content. For example, carbon nanotube containing hydrogels exhibited a six‐ to sevenfold increase in electrical conductivity (to 7 ± 2 mS/cm) at water content of 82%. It is demonstrated that at water content of 95 ± 2% the electrical behavior of multiwalled nanotube containing hydrogels transitions (percolates) from transport dominated by ions (owing to GG) to transport dominated by electrons (owing to the carbon nanotube network). © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 864–871     

Division closed partially ordered rings

Fuchs called a partially-ordered integral domain, say D, division closed if it has the property that whenever a > 0 and ab > 0, then b > 0. He showed that if D is a lattice-ordered division closed field, then D is totally ordered. In fact, it is known that for a lattice-ordered division ring, the following three conditions are equivalent: a) squares are positive, b) the order is total, and c) the ring is division closed. In the present article, our aim is to study \({\ell}\)-rings that possibly possess zerodivisors and focus on a natural generalization of the property of being division closed, what we call regular division closed. Our investigations lead us to the concept of a positive separating element in an \({\ell}\)-ring, which is related to the well-known concept of a positive d-element.     

Photoelastic tests on complex intersections of reinforced thin-shell cylinders

This paper presents the three-dimensional photoelastic analyses accompanied by extensive finite-element studies of several thin-shell pressure vessels with various cylindrical intersections. The models consisted of right circular cylindrical shells with diameter-to-thickness ratios of 220, reinforced with circumferential, longitudinal and diagonal T-stiffeners. The cylindrical shells and stiffeners were intersected by various smaller cylinders producing complex intersection joints which included radial and angular fillets. Each of the models was constructed from 80 to 150 parts prepared from flat sheets, “contour-cast” shells, and milled machined parts. The model techniques as well as the machining, assembling and testing methods of the pressure vessels are presented.     

Fracture energy for three-point-bend tests on single-edge-notched beams

Three test series of single-edge-notched beams in three-point bending are conducted to evaluate the fracture energy of concrete. The fracture energy is determined from the area under the complete load: load-point deflection diagram. The nonlinear fictitious crack model is implemented in a finite-element analysis showing good agreement with the experimental data. By varying the notch depth and the beam depth it is shown that the fracture energy, traditionally presented as a material property, depends upon the specimen size and configuration. This is atributed to the energy dissipation in the process zone which is not accounted for in the analytical model.     

An automated process for three-dimensional photoelastic analysis

The use of two monochromatic light sources to obtain two isochromatic patterns permits a fully automated shear-difference analysis of the stress distribution in a three-dimensional photoelastic model. A development is given of the logic necessary to process the data taken from an automated polariscope as well as the design details of the polariscope.